Distance-based regression analysis is a method used to find connections between different variables in genetic studies and other research fields. A new statistical test called pseudo-$F$ was created to analyze these relationships, but it has limitations. Researchers have now developed a more powerful test called square-root $F$-type test, which improves upon the original test. By studying the behavior of these tests, they found that the new test has better performance, especially when the variables are highly correlated. This was confirmed through simulations using a gene expression dataset related to prostate cancer.